金融网络中的敏感性和计算复杂性
Sensitivity and Computational Complexity in Financial Networks
摘要：
现代金融网络表现出高度的相互关联性，确定金融网络不稳定和蔓延的原因对于制定政策和避免未来的金融崩溃是必要的。在《美国经济评论》（American Economic Review）上，艾略特、戈卢布和杰克逊提出了一个简单的模型，用于捕捉复杂金融网络的动态。在艾略特、戈卢布和杰克逊的模型中，网络中的每个机构都可以购买其他机构的基础资产或百分比股份（交叉持股），如果任何机构的价值低于临界阈值，其价值就会遭受额外的失败成本。这项工作表明，即使在艾略特，戈卢布和杰克逊提出的简单模型中，也存在理解网络固有风险的根本障碍。首先，如果不要求机构保持最低限度的自我持有量，那么单个机构投资的$ε$变化可能会对系统中机构的净资产产生任意放大的影响。这一敏感性结果表明，如果机构有小的自我持有，那么估计一个机构的市场价值需要几乎完美的信息，系统中的每一个交叉持有。其次，我们表明，即使监管机构有完整的信息，所有的交叉持有系统中，它可能是计算上难以估计的故障，可能会造成一个任意小的冲击系统。总之，这些结果表明，交叉持股或标的资产价值的任何不确定性都可以被网络放大，成为网络中机构估值的任意大的不确定性。
英文摘要：
Modern financial networks exhibit a high degree of interconnectedness and determining the causes of instability and contagion in financial networks is necessary to inform policy and avoid future financial collapse. In the American Economic Review, Elliott, Golub and Jackson proposed a simple model for capturing the dynamics of complex financial networks. In Elliott, Golub and Jackson's model, each institution in the network can buy underlying assets or percentage shares in other institutions (cross-holdings) and if any institution's value drops below a critical threshold value, its value suffers an additional failure cost. This work shows that even in simple model put forward by Elliott, Golub and Jackson there are fundamental barriers to understanding the risks that are inherent in a network. First, if institutions are not required to maintain a minimum amount of self-holdings, an $ε$ change in investments by a single institution can have an arbitrarily magnified influence on the net worth of the institutions in the system. This sensitivity result shows that if institutions have small self-holdings, then estimating the market value of an institution requires almost perfect information about every cross-holding in the system. Second, we show that even if a regulator has complete information about all cross-holdings in the system, it may be computationally intractable to even estimate the number of failures that could be caused by an arbitrarily small shock to the system. Together, these results show that any uncertainty in the cross-holdings or values of the underlying assets can be amplified by the network to arbitrarily large uncertainty in the valuations of institutions in the network.
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